In an amateur’s nutshell they refer to the thyroid hormones, and whether or not they are roaming “free” through the blood, or are bound up with another compound.
The thyroid makes two essential hormones: T4 is thyroxine. One endocrinology book I read called T4 a “prohormone” because it needs to be changed to T3 before it can do its work. The “4” refers to the fact that there are four atoms of Iodine in it. The vast majority of the output of the thyroid gland is T4. T3 has 3 atoms of iodine. This is the hormone from the thyroid that is responsible for cell metabolism throughout the body.
The vast majority of the thyroid hormone, whether T4 or T3, that is in our blood at any given time is bound to other chemicals or protein compounds. And being bound up actually prevents them from entering into cell metabolism. It is the FREE, or unbound, hormone that activates cell metabolism, so the numbers on this become important when we are hyperthyroid.